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What does factorially mean?

Looking for the meaning or definition of the word factorially? Here's what it means.

Adverb
  1. (mathematics) According to a factorial series or ratio.
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These three features were factorially crossed to yield eight stimulus categories, one of which was not used.
The shortened 18-item scale is both more reliable and more factorially pure than the original 25-item measure with which it correlates at a.93 level.
The BES is a factorially derived measure of male and female body esteem.
Factor analytic method was used to validate the questionnaire and was found to be factorially pure.
These two two-level treatments were combined factorially, leading to the following four combinations.
Three stimulus frequencies were combined factorially with two input channels and three measurement procedures.

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